The Developmental Dynamics of Terrorist OrganizationsAaron Clauset1,2,3*, Kristian Skrede Gleditsch4,51 Department of Comp...
Patterns in global conflictA pattern-based approach to studying conflict owes much to theseminal work in the early 20th ce...
adds internal independent production lines (terrorist cells), theeffective time between new events falls even though eachp...
these militant activities. However, so long as recruitment continuesto grow the number of militant cells, the positive fee...
Oklahoma), and DFI International’s research on terrorist organi-zations. In 2008, however, the U.S. Department of Homeland...
delay and experience for both deadly and non-deadly attacks.Using a linear regression model rather than ordered logit does...
achieve k~12 events, the median total calendar time between thefirst and twelfth event is 4:4 years. Similar results hold ...
and with m, s estimated using maximum likelihood given the fixedb value, we find that the value of ^bb is highly statistic...
loop is a generic ‘‘developmental’’ trajectory: as an organizationages, it tends to produce violent events more and more q...
production rates. The progressive loss of organizations could bedue to high rates of organizational death, e.g., from coun...
5. Brown D, Dalton J, Hoyle H (2004) Spatial forecast methods for terrorist eventsin urban environments. Lecture Notes in ...
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Clauset (2012) the developmental dynamics of terrorist organizations

  1. 1. The Developmental Dynamics of Terrorist OrganizationsAaron Clauset1,2,3*, Kristian Skrede Gleditsch4,51 Department of Computer Science, University of Colorado, Boulder, Colorado, United States of America, 2 BioFrontiers Institute, University of Colorado, Boulder,Colorado, United States of America, 3 Santa Fe Institute, Santa Fe, New Mexico, United States of America, 4 Department of Government, University of Essex, WivenhoePark, Colchester, United Kingdom, 5 Centre for the Study of Civil War, Oslo, NorwayAbstractWe identify robust statistical patterns in the frequency and severity of violent attacks by terrorist organizations as they growand age. Using group-level static and dynamic analyses of terrorist events worldwide from 1968–2008 and a simulationmodel of organizational dynamics, we show that the production of violent events tends to accelerate with increasing sizeand experience. This coupling of frequency, experience and size arises from a fundamental positive feedback loop in whichattacks lead to growth which leads to increased production of new attacks. In contrast, event severity is independent ofboth size and experience. Thus larger, more experienced organizations are more deadly because they attack morefrequently, not because their attacks are more deadly, and large events are equally likely to come from large and smallorganizations. These results hold across political ideologies and time, suggesting that the frequency and severity ofterrorism may be constrained by fundamental processes.Citation: Clauset A, Gleditsch KS (2012) The Developmental Dynamics of Terrorist Organizations. PLoS ONE 7(11): e48633. doi:10.1371/journal.pone.0048633Editor: Petter Holme, Umea˚ University, SwedenReceived August 21, 2012; Accepted October 2, 2012; Published November 21, 2012Copyright: ß 2012 Clauset, Gleditsch. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Funding: This work was supported in part by the Santa Fe Institute, the Economic and Social Research Council (RES-062-23-0259), and the Research Council ofNorway (180441/V10). These sources provided support for the authors’ salaries alone. The funders had no role in study design, data collection and analysis,decision to publish, or preparation of the manuscript.Competing Interests: The authors have declared that no competing interests exist.* E-mail: aaron.clauset@colorado.eduIntroductionMuch research on patterns in terrorism has been inspired byparticular historic events and ‘‘waves’’ of specific forms of terroristattacks [1,2]. Just as the rise in international skyjackings in the1970s led to a resurgence of studies of terrorism, the 11 September2001 attacks renewed interest in why groups resort to terrorism,the specific choice of attack targets, and the relative effectiveness ofparticular counterterrorism measures. As a result, many research-ers have developed typologies of specific forms of terrorism andhighlighted the distinctiveness of different terrorist groups. Bycontrast, in this manuscript we examine whether there arefundamental patterns in the frequency and severity (number ofdeaths) of deadly events carried out by terrorist organizations andwhat mechanisms might generate them.Little research on terrorism has focused on directly modelingindividual event frequency and severity, and the way these changeover an organization’s lifetime. When deaths are considered, theyare typically aggregated and used as a covariate to understandother aspects of terrorism, e.g., trends over time [3,4], the when,where, what, how and why of the resort to terrorism [5–7],differences between organizations [8], or the incident rates oroutcomes of events [3,9]. Such efforts have used time seriesanalysis [3,4,9], qualitative models or human expertise of specificscenarios, actors, targets or attacks [10] or quantitative modelsbased on factor analysis [11,12], social networks [13,14] or formaladversarial interactions [6,15,16].Our approach is different and complementary to theseapproaches, focusing on global trends and patterns in thefrequency and severity of events [17–25], rather than on eventparticulars or motivations. By focusing our analysis at the globalscale, the importance of individual decisions in specific contexts isin fact lessened, due to the central limit theorem and the roughindependence of individual events; as a result, the importance ofgeneric non-strategic processes is enhanced and these processes, ifany, may be studied. Explanations of such patterns must thus focuson processes or constraints that are independent of variations incontext or specific motivation and may include physical con-straints, network effects and endogenous population dynamics,which are well suited to explain the behavior of strategicallyunco¨ordinated populations of actors [24]. This approach toinvestigating the fundamental laws of terrorism has much incommon with that of statistical physics, in which the self-averagingproperties of independent events allows for interesting population-level properties to emerge from microscopic system chaos. Thisstatistical physics-style approach is increasingly being applied tostudy complex social systems [26–28], yielding a number of novelinsights.Here, we aim to shed new light on the fundamental processesgoverning the frequency and severity of terrorist events bystudying their statistical relationship with the organizations thatgenerate them. Our aim is to identify global patterns in theserelationships and to explain their origin mechanistically. Weemploy a combination of disaggregated data analysis, studying alarge database of terrorist events worldwide from 1968–2007,statistical modeling and inference, computational modeling andregression analysis to validate our mechanistic hypotheses. Byshedding new light on these large-scale patterns and trends interrorism, and on how such patterns emerge from local-levelbehaviors, this large-scale statistical or pattern-based approach cansupplement formal models of strategic interactions, informcounter-terrorism policy and clarify our general ability to forecastor anticipate future terrorist events or trends.PLOS ONE | 1 November 2012 | Volume 7 | Issue 11 | e48633
  2. 2. Patterns in global conflictA pattern-based approach to studying conflict owes much to theseminal work in the early 20th century of Lewis Fry Richardson–aphysicist and meteorologist known for collecting data on conflicts(‘‘deadly quarrels’’), modeling arms races using differentialequations, as well as early contributions to understanding thefrequencies and severities of wars. Specifically, Richardson [29,30]identified the remarkable pattern that the frequency of wars decayslike the inverse power of their severity. (Power-law distributionscan indicate unusual underlying or endogenous processes, e.g.,feedback loops, network effects, self-organization or optimization.From a purely statistical perspective, power-law distributionsgenerate large events orders of magnitude more often than wewould expect under a Normal assumption. Recently, power-lawdistributions have been identified in a wide range of social andbiological systems [31]. See [32], [33] and [34] for reviews, orAppendix A of [35] for a gentle introduction.) This empiricalpattern implies that there is no fundamental statistical differencebetween rare but catastrophic wars and more common but lesssevere wars–the likelihoods of both are described by a singlemathematical function:Pr (event with severity x) ! x{a,where x counts the number of fatalities (severity) and a is the‘‘scaling exponent,’’ which controls how quickly the frequencydecreases as severity increases. It also implies that the underlyingsocial and political processes for both large and small wars may befundamentally the same, i.e., large wars may simply be ‘‘scaledup’’ versions of small wars. In general, the identification of a powerlaw implies that studying the statistically more common events canshed light on certain aspects of extremely rare events. (Seismol-ogists study large earthquakes in this way: the frequencies of bothlarge and small quakes follow a power-law distribution, called theGutenberg-Richter Law, and the physical processes that generateboth small and large quakes are fundamentally the same).Recently, Clauset et al. [20,31] showed that this same pattern–apower-law, ‘‘Richardson’s Law’’–also holds for the frequency ofsevere terrorist attacks (reported fatalities) worldwide, while [23]suggest a similar pattern for events within insurgencies. Thepower-law pattern in terrorism is highly robust: it persists over thepast 40 years despite large structural and political changes in theinternational system and is independent of the type of weaponused (explosives, firearms, arson, knives, etc.), the emergence andincreasing popularity of suicide attacks, the demise of manyindividual terrorist organizations, and the economic developmentof the target country.Thus, fundamental regularities in terrorism can and do emergeat the global level despite the highly contingent and context-specific nature of the individual attacks, conflicts and decisions.Insights into how these patterns’ arise will likely shed new light onthe underlying social or political processes that drive and constrainglobal trends and on effective policies for responding to ormanaging those processes.MethodsWe consider the frequency and severity of attacks over thelifetime of individual terrorist organizations, and the question ofwhether organizations exhibit common statistical patterns in thesebehaviors. We argue that organization size (number of personnel)plays a fundamental role in limiting the overall frequency, but notthe severity, of violent events by a group. The key idea is thatorganization size and its overall production rate of events arelinked. If events lead to growth in any way, then this link implies apositive feedback loop in which each attack increases theproduction rate of future attacks. Thus, a terrorist organizationcan be viewed as a kind of factory whose principal product ispolitical violence, and whose proceeds are reinvested in increasedproduction capacity.To test these ‘‘developmental dynamics’’ hypotheses, we presentnovel statistical analyses of the behavior of nearly 400 terroristorganizations worldwide over the period 1968–2008. We findstrong evidence for precisely this kind of generic acceleration inevent production. This supports the notion that an organization’savailable labor, i.e., the size of its militant wing, is a fundamentalconstraint on the overall frequency of its attacks. We further showthat the rate at which an organization cycles through the positivefeedback loop can depend on covariates like its political ideology,with religiously-motivated organizations accelerating (growing) thefastest. In contrast, we find no evidence that event severity dependson organizational size or experience. Instead, the distribution ofattack severities follows a rough form of Richardson’s Lawindependent of size, experience or political motivation.These results imply that very large events are equally likely to begenerated by small groups as by large groups, and that largerorganizations are indeed more deadly [8], not because theirindividual attacks are systematically more spectacular but becausethey typically carry out many more attacks. That is, the size of thebeast directly determines the overall level of terror activity(frequency) but not the quality (severity) of those actions.Recently, Johnson et al. [25] used a similar approach to analyzethe timing of events in the Iraq and Afghanistan conflicts, whichwas in turn based on an earlier version of this manuscript [22].Although similar statistical patterns to the ones we describe herewere observed in those conflicts, a different explanation wasoffered for their origin. We will revisit this comparison andcomment on the problems our statistical results pose for theexplanation offered by [25].Impact of Size on FrequencyH1 Labor-constraints: the overall production rate of violentevents by an organization depends on its size, and thus thetime between consecutive attacks Dt is roughly inverselyproportional to the size s of the organization. Mathemati-cally, s/1/Dt.In other words, the production of terrorist events cannot beautomated. If this were possible, organizations could producearbitrary numbers of events without needing to grow in size, muchlike a fully automated factory requires essentially no humanpersonnel to function. (In this light, cyber terrorism is an interestingcase: it remains unclear to what degree the planning and executionof cyber terrorist attacks can be done automatically, by computers.Our current belief is that cyber terrorism is also not massproduceable and thus some labor constraint will persist, althoughit may be substantially lessened relative to physical terrorism).Instead, we argue that each terrorist event requires significanthuman involvement, e.g., to conceive, plan and execute it. Thisrequirement for human effort implies that for the production rateof an organization to decrease, it must add additional members toproduce them. And, the resultant increased rate occurs notbecause more hands make any individual event proceed morequickly, but because multiple events may be carried out in parallel.That is, the overall production rate of the organization is like theproduction rate of an entire factory; as the factory (organization)Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 2 November 2012 | Volume 7 | Issue 11 | e48633
  3. 3. adds internal independent production lines (terrorist cells), theeffective time between new events falls even though eachproduction line operates at a constant rate.It is important to recognize that H1 does not imply that the onlyway to increase the group-level production rate of attacks isthrough organizational growth. Indeed, many aspects of eventproduction surely do benefit from technology or efficiencyimprovements [36–39]. Instead, H1 implies that such factors canonly moderate, not eliminate, the fundamental constraint that sizeplaces on production. To the extent that these factors decrease thetime between an organization’s events, the literature on learningsuggests that the overall impact will be modest [39]. In contrast,increases in labor, which allow many terrorist cells to operate inparallel, can lead to much larger improvements.Finally, we note that this constraint should be strongest for smallorganizations, who likely have the worst access to efficiency-improving resources like specialized personnel, training facilities orfactories and who may reap the largest benefit, e.g., mediavisibility, from striving to maximize their event production.Because most organizations begin small and grow over time, thisshould be most evidence early in the lifetime of an organization. (Aspatial corollary of H1 is that if an ‘‘organization’’ is defined asthose militants within some geographic locale, e.g., a province ordistrict, then the frequency of events within that locale will beroughly inversely proportional to the number of militants there.That is, the s!1=Dt relationship should hold when both s and Dtare defined by a geographic boundary. Organizational ‘‘growth’’can then be understood as either immigration or recruitment ofnew militants).Events, Recruitment and GrowthWhat role do attacks play in changing organizational size? If anevent gains the organization wider visibility among potentialmembers or sympathizers, the organization may grow in size as aresult of that event. (Decreases in size are likely driven by distinctsocial processes (see [40]), which we do not consider here).H2 Event-recruitment: organizational growth (increased s) ispartly driven by recruitment associated with the productionof new events (increased k), i.e., events lead to recruitmentwhich leads to organizational growth. Mathematically, ds/dk.0.H2 does not imply that growth comes only from violence-related recruitment. So long as recruitment is partly based on theproduction of violent events, H2 implies a correlation betweenincreases in size and increased event production.Frequency AccelerationTogether, H1 and H2 imply a positive feedback loop in whichattacks lead to recruitment which leads to organizational growthand thus an increased group-level production of new attacks. Solong as a portion of the growth is allocated to producing additionalevents, i.e., so long as the militant wing grows with the overallorganization, H1 and H2 jointly imply H3.H3 Frequency-acceleration: as an organization carries out moreattacks (increased k), the time between subsequent attacks Dtdecreases. Mathematically, dDt/dk,0.That is, H1 predicts s!1=Dt while H2 predicts ds=dkw0.Eliminating the common factor of s yields the prediction thatdDt=dkv0, in which the continued production of violent eventsproduces a decreasing delay between those events. (This dynam-ical relationship produces a similar pattern to that observed in‘‘learning’’ or ‘‘progress curves,’’ in which continued productioncovaries with lowered production costs or time [36,39,41].Although the pattern is similar, the mechanism is different).Impact of Size on SeverityIncreased size may bring greater access to capital and skilledlabor, e.g., experienced professionals, advanced arms, intelligence,etc., and thus more spectacular attacks.H4 Severity-increase: the severity x of a new attack increaseswith organizational size s and, via H2, the number of attacksk. Mathematically, dx/ds.0 and dx/dk.0, respectively.Combined with H2, H3 implies that attacks by experienced,larger groups should be consistently and significantly more deadlythan those of less experienced or smaller groups.H4 assumes a tangible benefit for maximizing the severity ofattacks, e.g., to gain wider visibility for the organization’s cause orto demonstrate power or resolve. Such incentives are not foregoneconclusions: severe attacks may also attract harsh attention fromstate-level actors, leading to repression, police action or thedestruction of physical or financial resources. They may alsoinduce counter-productive effects on potential sympathizers, e.g.,due to the shockingness of spectacular events. As a result, weconsider the theoretical argument supporting the severity-increasehypothesis to be marginal.ResultsModel of terrorist organizationsTo illustrate these interactions between an organization’s sizeand the frequency and severity of attacks over its lifetime, weconstruct a simple model of a terrorist organization’s development(see Figure 1 for a schematic).Historically, terrorist organizations begin as a small collectionsof terrorism-inclined individuals [42]. Let this initial collection becomposed of roughly g individuals, which denotes the typical orcharacteristic size of a terrorist cell. The particular value of g is notimportant, but may depend political ideology, socio-economiccontext [43], the attack’s target, etc. The cell plans and conductsits first attack, which gains it some visibility, via either traditionalmedia coverage or informal channels. Subsequent recruitmentyields a number of additional members n (H2), and now theorganization is larger. Again, the particular value of n is notimportant, but likely depends on context-specific factors.Each cell continues planning and carrying out new attacks,roughly once every t days (H1). Newly recruited members formnew cells, of size g (H1) and new cells plan and carry out their ownattacks in parallel. It is this parallelism that allows the largerorganization to appear to be acting more quickly, even though theplanning time t for any particular event remains fixed. An attackby any cell leads to overall organizational growth via recruitment(H2), which in turn increases the organization’s overall productionrate of attacks by adding new cells (H3). Finally, as the groupgrows, the increased manpower also increases its ability to carryout more severe events (H4), e.g., because more supporting rolesallow better surveillance, access to better equipment, etc.Coordinating the activities of these additional individuals, or thedevelopment of non-violent initiatives like a political wing or theprovision of social services, will draw some members away fromDevelopmental Dynamics of Terrorist OrganizationsPLOS ONE | 3 November 2012 | Volume 7 | Issue 11 | e48633
  4. 4. these militant activities. However, so long as recruitment continuesto grow the number of militant cells, the positive feedback loopremains.This simple model intentionally omits many factors, such asorganizational structure, political motivation, geography, etc., thatare likely to impact the behavior of any particular organization.We also intentionally omit any potential response by state-levelactors and their consequences on the organization’s evolution.This last decision is made in order to focus on the development ofthe organization, i.e., its early lifetime, where labor constraints arelikely most profound, although such processes could naturally beadded. Omitting these factors keep the model simple and allows usto make quantitative predictions of the generic relationshipbetween organization size and the frequency and severity of itsattacks via direct numerical simulation. To mimic the naturalvariation between particular events, for each new event beingplanned by a cell, we draw a delay t from a fixed distribution. (Ingeneral, our results hold so long as the distribution of t is well-behaved and stationary with respect to k.) Specification details andcomputer code for the simulation are given in Text S1.Each simulated terrorist organization generates a uniquesequence of events representing the collective behavior of its cellsover time, and we extract the generic behavior by computingquantiles over variables of interest for many such simulatedorganizations. Here, we are interested in how the delay betweensubsequent attacks Dt varies with cumulative number of events k(H3), and how the size of the organization, measured by thenumber of cells s=g varies with calendar time t from the first event(H2). H4 predicts that event severity correlates with organizationsize and thus no additional information is gained by explicitlysimulating event severities.Figure 2 shows the results for 10,000 simulated organizations,for three choices of the ratio n=g, which represents the growth rateof the organization’s militant wing. When n=gv1 regime,organizational growth is slow because multiple events are requiredto establish a new terrorist cell; but, when n=gw1, organizationalgrowth is fast because each event produces at least one new cell.The generic behavior of our model is clear: (i) organizationalsize grows exponentially with time, at rate n=g, and (ii) thefeedback between size and production rate induces a strongcorrelation between experience, size and the frequency of events.Finally, the model produces a universal functional relationshipbetween delay Dt and cumulative production k of the formDt!k{1, and this relationship is independent of the growth raten=g.This latter point is worth reiterating: so long as each new eventleads to some marginal increase in the overall production rate(H2), a positive feedback loop between size and event productionwill exist. This feedback will be linear Dt!k{1if the growth raten=g does not vary with experience k. If the militant wing is adecreasing fraction of the overall organization (n=g decreases overtime), the feedback will be sub-linear and k{bwith bv1, while ifit increases with time, the feedback will be super-linear and bw1.These properties imply that if a growing organization doesprovoke responses from state-level actors, these responses will notbreak the feedback loop unless they succeed in both limiting thegrowth and reducing the size of the organization, a point to whichwe will return later.These quantitative predictions can be tested with empirical databy examining Dt as a function of k across many organizations. IfDt!k{1holds in the data, we have strong evidence for preciselythe size-mediated feedback loop described here.Empirical dataOrganizational size data were drawn from the Big Allied AndDangerous (BAAD) data set [8], which offers the currently bestavailable size estimates for terrorist organizations worldwide.Other sources of size data lack the breadth or temporal resolutionfor accurate analysis. For instance, the START program and theMIPT database previously held a small number of estimates ofuncertain accuracy, generated by Detica, Inc., a British defensecontractor, and [44] compiled a database of information on 649terrorist groups that included only estimates of the maximum sizeover a group’s entire lifetime. The BAAD data were generated bya survey of domain experts at the Monterey Institute ofInternational Studies (MIIS) who estimated the rough order ofmagnitude (1–100, 100–1000, 1000–10,000 and w10,000 per-sonnel) of the maximum size achieved by each of 381 groups,between 1998 and 2005, identified in the [45] event database. Ofthese, 161 organizations conducted at least one deadly attack, and80 conducted at least two in that period.To ensure good compatibility with this organization list, eventdata were drawn from the MIPT Terrorism Knowledge Base [45],which contained 35,668 terrorism events, of which 13,274 resultedin at least one fatality, as of 29 January 2008. (Other sources ofevent data include the Global Terrorism Database [46], theWorldwide Incident Tracking System [47] and the ITERATEdata [48]. We note that neither these nor the MIPT databaseprovide complete and consistent worldwide coverage.) For theperiod 1968–1997, the MIPT database includes mainly interna-tional events involving actors from at least two countries, while for1998–2008 it includes both domestic and international eventsfrom much of the world. (The MIPT data were originally drawnfrom the RAND Terrorism Chronology 1968–1997, the RAND-MIPT Terrorism Incident database (1998–Present), the TerrorismIndictment database (University of Arkansas & University of∆t ∝ 1/ss → s + ηx ∝ sFigure 1. A model of terrorist organizations. A schematic illustrating the feedback loop relationship between size s and the frequency andseverity of attacks: the delay between subsequent attacks Dt is inversely related to an organization’s size s while the severity of subsequent attacks xgrows with s; new events lead to recruitment which leads to growth, which increases the size variable s.doi:10.1371/journal.pone.0048633.g001Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 4 November 2012 | Volume 7 | Issue 11 | e48633
  5. 5. Oklahoma), and DFI International’s research on terrorist organi-zations. In 2008, however, the U.S. Department of HomelandSecurity discontinued its funding for the maintenance of thedatabase in favor of the University of Maryland’s START center’sGlobal Terrorism Database [46].) Each event is defined as anattack on a single target in a single location (city) on a single day.For example, the Al Qaeda attacks in the United States on 11September 2001 appear as three events in the database, one foreach of the New York City, Washington D.C. and Shanksville,Pennsylvania locations. Each record includes the date, target, city(if applicable), country, type of weapon used, terrorist group(s)responsible (if known), number of deaths (if known), number ofinjuries (if known), a brief description of the attack and the sourceof the information.The organizations identified in the MIPT database are asuperset of those contained in the BAAD data set, and we will usethese additional data analyses that do not require size estimates.For each organization, we extracted the full sequence of itsattributed or claimed events. This yields 10,335 events worldwidefrom 1968–2008 associated with 910 identifiable organizations.For each of the 1,204 events worldwide with unknown severity, weassign a severity of x~0 to preserve timing information. Further,because of the day-level temporal resolution of events in thedatabase, multiple events on the same day by the same group haveambiguous ‘‘delay’’ (inverse frequency). We eliminate this ambi-guity by aggregating such events into a single ‘‘event day’’ withseverity equal to the sum of the component severities. This slightlyreduces the number of events, mainly for the most activeorganizations late in their life history. As a consequence, theminimum resolvable delay in the database for two events by thesame organization is Dt~1 day.Regression modelsBefore analyzing the evolution of attacks by individualorganizations we conduct static or cross-sectional regressionanalysis at the level of individual organizations. We examine therelationship between group size and attack patterns, in particularthe delay between attacks, the experience of a group in terms ofnumber of events, and the severity of attacks.To recap, we expect larger groups to generate a larger numberof attacks, have shorter delays between attacks (H1), and generatemore severe attacks even accounting for other attack patterns (H4).We can evaluate H1 by comparing maximum group size s fromBAAD and the minimum delay between attacks Dt in MIPT. Wecan assess H4 by comparing size and the maximum severity x ofattacks. Finally, H2 implies that larger groups should have highermaximum experience k or cumulative number of events. (H3,postulating a declining delay with subsequent attack, cannot beevaluated with static data; we return to this point later).Although group size should predict attack patterns, individualmeasures such as maximum severity will be at least in part afunction of the total number of attacks. That is, for anydistribution of severities, an increased production rate (samplingintensity) will naturally inflate the maximum severity over a fixedtime period, even if the distribution is stationary. Thus, in order toexamine the partial relationship between size and the relatedattack variables–or their independent predictive value on size oncewe take into account the other attack pattern characteristics–it ismore convenient to consider to what extent we can account forsize as function of the attack measures.We use an ordered logit regression model of size since theBAAD data give order-of-magnitude estimates of maximum size.As the BAAD data pertain to the time period 1998–2005, werestrict our attack pattern measures to attacks during this sametime period. Since the distributions of minimum delay, maximumexperience, and maximum severity are all highly skewed we takethe natural logarithm, adding 1 to severity to prevent taking thelog of 0 in the case of non-fatal events. We report the empiricalestimates in Table 1.The results display a significant negative relationship betweenfatal attack delay and group size, consistent with our claim thatlarger groups will have shorter delays between attacks (H1). Wealso find a positive relationship between group size andexperience, consistent with our claim that larger groups generatea higher number of attacks (H2). Finally, the maximum severity ofthe attacks is not significantly related to group size, once we havecontrolled for delay and experience variables. This contradicts thehypothesis that larger groups are systematically more likely togenerate severe attacks (H4). Overall, the model places 58.75% ofall the groups in the correct bins for group size. Only 5% of theobservations are badly mis-classified, with predictions off by morethan one order of magnitude. By contrast, a null model predictingall groups to have the modal size category (100{1000) onlyclassified 43.75% of the observations correctly. (We considered anumber of alternative specifications. Severity remains an insignif-icant predictor of group size when we consider combinations ofFigure 2. Simulated development of a terrorist organization. (A) Median event delay Dt vs. cumulative number of events k, for 10,000simulated terrorist organizations and three choices of the number of cells v/g added per event. Dashed line shows the function Dt/k21, from Eq. (1).(B) Median size (number of terrorist ‘‘cells’’ s/v) vs. calendar time from the first event, showing exponential growth with rate set by v/g.doi:10.1371/journal.pone.0048633.g002Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 5 November 2012 | Volume 7 | Issue 11 | e48633
  6. 6. delay and experience for both deadly and non-deadly attacks.Using a linear regression model rather than ordered logit does notchange our substantive conclusions).Since the BAAD data cover only about half of the identifiableorganizations in the MIPT database over a restricted time span(1998–2005), we conduct a supplementary analysis with the fullMIPT dataset, where we consider how a group’s total experiencecan be accounted for by differences in minimum delay andmaximum attack severity. (We limit the analysis to MIPTorganization that generated at least two events (frequency) andone deadly event (severity); only 167 organizations satisfy thesecriteria.) Table 2 report the results for a linear regression withlogged values for all the terms for fatal (F) and all attacks (A,including non-fatal attacks) experience respectively. The resultsclearly show that the minimum delay is a significant predictor ofgroup experience, and they mildly support the claim aboutseverity, as the positive coefficient for severity is significantlydifferent from 0. However, comparing the change in the R2forestimating the model with and without the severity and delayterms respectively indicates that dropping the severity variableleads to a relatively small decline, while the impact of omitting thedelay variables is substantial. Hence, variation in delay betweenattacks accounts for much more of the variation in experience thandoes severity.These static analyses provide substantial preliminary evidencein support of H1 and H2 and little evidence to support H4. Wenow go beyond static analyses and test our predictions for allorganizations in the MIPT database using a novel dynamicalanalysis tool called a ‘‘development curve’’.Developmental dynamicsA development curve is a statistical tool that measures theevolution of organization behavioral variables along a commonquantitative timeline [22]. It is similar in structure and use to the‘‘experience’’, ‘‘learning’’ and ‘‘progress curves’’ sometimes used inmanagement science [36,39] to quantify the relationship betweenper-item production cost (or time) and ‘‘experience’’ (cumulativeitem production). Because we study behavioral variables ratherthan the costs of production, and to explicitly avoid implyinglearning-based mechanisms, we choose a distinct term. Theanalysis of these developmental curves facilitates direct compar-isons of the behaviors of different groups at similar points in theirlife histories, which is useful for testing our hypotheses.We instrument a common timeline using organizationalexperience k, defined as the cumulative number of eventsproduced by or associated with a particular organization, andwe compare the delay Dt between the kth and (kz1)th events, orthe severity x of the kth attack, across all organizations in oursample. For each of the 910 organizations, we extract from theMIPT event data an ordered sequence of coordinatesf(1,z1),(2,z2), . . .g, which represent the group’s behavioral trajec-tory on the variable z over its lifetime. The visualization of suchtrajectory is typically made using double-logarithmic axes, asillustrated in our simulation results in Figure 2. Although the curveconstruction itself ignores details such as the date of anorganization’s first attack, its location, ideology, etc., thesevariables can be used for subsequent analysis, e.g., comparingthe trajectories across covariates.Constructing a development curve for an individual organiza-tion (see Text S1) can facilitate the investigation of specificbehavioral dynamics of individual groups over their lifetimes.However, the specific factors associated with particular organiza-tions may obscure the generic tendency embodied by ourhypothesis. To investigate these, we examine the averagetrajectory across many organizations by tabulating the conditionaldistribution Pr (DtDk) of delays, for a specified level of experiencek. Thus, an organization that has carried out kÃevents contributesto each of the kƒkÃconditional distributions. This approachprovides a strong test of the frequency-acceleration (H3) andattack-severity hypotheses (H4) predictions.Frequency of attacks over time. Figure 3A shows thecomposite frequency curve for all organizations in our study. Toreduce the overprinting effects of showing the trajectories for somany organizations, we bin the values of k on a logarithmic scaleand plot the mean and 1st and 3rd quartiles of the data withineach bin. Remarkably, the observed empirical pattern agrees veryclosely with our simulation model’s predictions (Figure 2).The progressive decrease of the delay distributions indicates ageneric tendency toward faster production with increased expe-rience for all types of organizations, in strong agreement with thefrequency-acceleration hypothesis (H3). But, the relationshipbetween delay and experience is not deterministic: not everyevent occurs more quickly than the last but the statistical tendencytoward shorter delays is clear.A terrorist organization thus typically begins in the low-frequency domain (large Dt) and moves in fits and starts towardthe high-frequency domain (small Dt). This trend is not subtle: themedian delay after the 1st event is Dt~124 days, while by the12th event, it has dropped to 35 days and by the 25th, the nextevent typically comes only 21 days later. This transition to fastproduction does take considerable calendar time: for groups thatTable 1. Ordered logit regression of group size, by fatalattack patterns.Variable ^bb SE(^bb)Delay: ln min(Dt) 20.351 0.119Experience: ln max(k) 0.707 0.193Severity: ln max(x) 0.150 0.159^aa0D1 20.163 0.840^aa1D2 2.652 0.895^aa2D3 5.039 1.056N = 80, LR x2= 41.42, df = 3, 58.75% correctly classified.doi:10.1371/journal.pone.0048633.t001Table 2. Linear regression of experience, by attack delay andseverity.Fatal attacks (F) All attacks (A)Variable ^bb SE(^bb) ^bb SE(^bb)DelayF: ln min(Dt) 20.119 0.042 20.110 0.040DelayA: ln min(Dt) 20.778 0.110 20.795 0.105DelayF6DelayA0.074 0.017 0.073 0.016Severity: ln max(x) 0.190 0.059 0.150 0.056^aa 3.115 0.236 3.336 0.225N = 167, R2= 0.545 N = 167, R2= 0.565R2(:severity) = 0.515 R2(:severity) = 0.546R2(:delay) = 0.222 R2(:delay) = 0.182doi:10.1371/journal.pone.0048633.t002Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 6 November 2012 | Volume 7 | Issue 11 | e48633
  7. 7. achieve k~12 events, the median total calendar time between thefirst and twelfth event is 4:4 years. Similar results hold for thetiming between deadly attacks.None of the sampled organizations progressively slowed theirattack rate over time, moving from high-frequency to low-frequency. A few unusual groups, such as Al-Qaeda in the Landof Two Rivers, begin and remain in the high-frequency domain.But, Al-Qaeda in the Land of Two Rivers is an interesting casebecause it is well-known to have operated under a different nameprior to 2004 [49]; thus, their initial high-frequency behavior canbe interpreted as support for the labor-constraint hypothesis (H1)because their initial larger size–a hold over from their previousidentity–allowed them to ‘‘begin’’ life (k~1) at a relatively highinitial production rate of attacks.Statistical model for the frequency ofattacks. Quantifying the dynamical relationship between delaysand experience allows us to go beyond our static analyses. To dothis, we statistically model the conditional distribution Pr (DtDk)from which delays are drawn and how this distribution varies withexperience.For these data, a truncated log-normal distribution, with thefollowing mathematical formPr (DtDk) ! exp{( log Dtzb log k{m)22s2" #, ð1Þprovides an excellent fit to the empirical delay data for allorganizations. Here, s2is the variance in delays at a given k, m isrelated to the characteristic delay between attacks and b controlsthe rate at which that delay decreases with increased experience k.That is, b governs the strength of the feedback loop betweenorganizational experience and the production of new events. Toinclude the effect of the minimum timing resolution Dt§1 presentin the empirical data, we force Pr (DtDk)~0 for Dtv1 day.This mathematical structure implies that the typical delaybetween attacks generically decreases according to a power-lawfunction with increasing experience.Dt&emk{b: ð2Þ(Details of this derivation are given in Text S1.) Thus, if bw0,we will observe a transition toward increasingly fast eventproduction, indicating support for H3. In contrast, if b~0,production rates do not vary with organizational experience, whileif bv0, production rates will decrease (larger Dt) with increasingexperience. In the bw0 regime predicted by H3, the accelerationeffect is dampened as the mean delay asymptotes to the minimumtiming resolution at Dt~1; this produces slight upward curvaturefor large values of k (see Text S1).The particular value of b has a strong effect on the materialdynamics of the feedback loop between increasing experience andincreasing production. If b~1, then the feedback loop is linear, asin our simulation model, and increases in organizationalexperience lead to proportional increases in event production.Linearity implies that the marginal growth associated with anadditional event is relatively constant over the organization’slifetime and a roughly constant fraction of new recruits areallocated to increase overall tempo of militant activities.In contrast, b?1 implies a non-linear feedback process.Notably, non-linear feedback processes are not common modelsof social processes (but see the literature on arms-races,particularly [17] and [50]). Traditional models often focus onproportional effects in which increases in one variable causeproportional changes in other variables. In non-linear feedbackprocesses, small increases in one variable can produce dramaticand continuing swings in other variables, leading to highlyunpredictable dynamics [51].When bw1, the feedback is super-linear, and one or both ofthese factors must increase with k. That is, either per-event growthin militant activities increases over time or an increasing fraction ofgrowth is allocated to militant activities. When bv1, the feedbackis sub-linear and the marginal recruitment benefits of new eventsdecrease over time or they are constant but recruits areincreasingly allocated toward non-militant activities.Fitting this model directly to the empirical data on all events, wefind that the maximum likelihood estimate is ^bb~1:0+0:1 (std.err.), indicating linear feedback. (This approach to estimating theparameter gives weight to the events early in organization’slifetime that is proportional to the number of such events in ourdata set; in contrast, a simple regression approach on the meandelays would bias the estimate by giving significant weight to therare but long-lived groups.) Using a Monte Carlo simulationagainst a null model with fixed b~0 (no acceleration over time)Figure 3. Timing of events. (A) Mean delay ,log Dt. between attacks, with 1st and 3rd quartiles, vs. group experience k. Solid line shows theexpected mean delay, from the statistical model described in the text. (B) A ‘‘data collapse’’ showing the alignment of the re-scaled conditional delaydistributions Pr (Dt:k^bbDk) with the estimated underlying log-normal distribution, as predicted by the model.doi:10.1371/journal.pone.0048633.g003Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 7 November 2012 | Volume 7 | Issue 11 | e48633
  8. 8. and with m, s estimated using maximum likelihood given the fixedb value, we find that the value of ^bb is highly statistically significant(pv0:001). (Fitting to deadly attacks alone yields a highlystatistically significant ^bb~1:1+0:2, slightly in the super-linearregime, but this value is statistically indistinguishable from b~1).A linear feedback implies that the marginal growth from event-driven recruitment does not vary much with organizational size orexperience. Furthermore, it implies that organizational learning interrorist groups [25,38], in which the production rate increasesdue to improved efficiency of a fixed number of individuals, playsa lesser role in explaining the overall acceleration of eventproduction than do the effects of increasing organizational size,because learning would mimic the effect of super-linear feedbackby allowing a constant number of militants to behave identically toan increasing number.A strong test of the statistical model’s plausibility is its predictionthat each of the k conditional delay distributions Pr (DtDk) is ascaled version of the underlying log-normal distribution LN(m,s2).To test this prediction, we re-scale the empirical distributions bythe predicted factor, i.e., we multiply each delay variable Dti byk^bbi , and then plot them against the estimated underlying log-normal distribution. A close alignment of these re-scaledconditional distributions, also called a ‘‘data collapse’’ [52], isstrong evidence for the hypothesized data model over a wide rangeof alternatives. Furthermore, for an alternative model to producesuch a data collapse requires that it follows the log-normal formclosely enough to be effectively equivalent. Figure 3B shows theresults of this test, illustrating an excellent data collapse, with eachof the re-scaled log-normal conditional distributions closelyaligning with the underlying log-normal form.These results also hold when we consider the developmentcurves for groups with a common political ideology (see Text S1).[53] divides the political motivations for terrorism into fourconventional categories: nationalist-separatist, reactionary, reli-gious and revolutionary. We coded according to Miller’s criteriathe 131 most prolific groups in our sample (all with k§10 deadlyevents), which accounts for 85% of events, and fitted Eq. (1) to thedata within each ideological category. Organizations with multiplepolitical motivations were placed in multiple categories, whichwould only lessen any differences between estimated parametersfor different categories. Within each of these categories, weobserve the same acceleration pattern, with the strongestacceleration (largest b) appearing for religious groups (Table 3).Severity of attacks over time. In contrast to the delaydevelopment curve, we find no statistically significant relationshipbetween the severity of attacks and increased experience (Pearson’sr~{0:024, t-test, p~0:17), indicating no support for the severity-increase hypothesis (H4). Across all organizations in our sample,the average severity of the first deadly event is SxT~6:7+0:9,which is only slightly larger than the average severity of deadlyevents by highly experienced groups (those with kw100)SxT~5:1+0:6. Figure 4A shows the composite severity curvefor all organizations in our study.As with the frequency curves, we find that the conditionalseverity distributions Pr (xDk) roughly collapse onto a single,underlying form (Figure 4B), which is similar to the power lawobserved for all deadly terrorist attacks worldwide from 1968–2008 [20,31]. That is, Richardson’s Law for terrorism appears tohold for both inexperienced and highly experienced groups.Combined with our static analysis of organizational size, thispattern implies a highly counter-intuitive fact: the severity ofattacks by larger, more experienced organizations, is notsignificantly greater than the severity of attacks by small,inexperienced organizations. That is, the common assumptionthat only experienced groups are capable of such mass destruction[54] is incorrect: inexperienced organizations are just as likely toproduce extremely severe events as highly experienced organiza-tions.However, although more experienced organizations are notsystematically more lethal at the individual-event level, theobserved frequency-acceleration pattern implies that more expe-rienced groups are significantly more lethal overall. This patternwas observed by [8] in their analysis of the BAAD organizations.Our results thus clarify their results, showing that the observedcorrelation between greater lethality (total deaths attributed to anorganization) and greater organizational size appears becauselarger, more experienced organizations produce events morequickly than smaller, less experienced organizations. It is thecumulative effect of the many small events that generates anincreased lethality, not a systematic increase in the lethality ofindividual events.Repeating this analyses on our ideology-coded set of organiza-tions, we find no systematic dependence of severity of attacks onorganizational experience within any of the ideological categories(see Text S1). That is, none of the model coefficients aresignificant, and the average severity of events within each categoryvary only a little. In short, we find that political ideology has nosystematic impact on the severity of events or the trajectory thatevent severities take over the lifespan of an organization.DiscussionAlthough details and circumstances vary widely across terroristorganizations, the generic nature of our results suggests generalconclusions. In particular, we find strong evidence for a positivefeedback loop among organizational size (number of personnel),experience (cumulative number of events) and the frequency atwhich that organization launches new events. Small andinexperienced organizations tend to produce events slowly, whilelarger and more experienced organizations tend to produce eventssometimes hundreds of times more frequently.Within this feedback loop, new attacks lead to organizationalgrowth and the corresponding increase in size leads to fasterproduction of new events because a larger size means moreterrorist cells are operating in parallel, not because eventsthemselves are planned more quickly. The result of this feedbackTable 3. Frequency curve parameters for organizations withsimilar political motivations.politicalmotivation groups events m s b significancenationalist-separatist55 2959 5.1(5) 2.2(1) 0.9(2) p,0.001reactionary 5 143 3.2(6) 1.8(2) 0.1(3) p,0.001religious 17 999 5(1) 2.4(5) 1.7(5) p,0.001revolutionary 53 2527 5.7(4) 2.3(2) 1.1(2) p,0.001all secular 883 6232 5.2(2) 2.25(9) 0.9(1) p,0.001all groups 910 7231 5.1(2) 2.32(9) 1.0(1) p,0.001Note: statistical significance estimated via Monte Carlo simulation of a two-tailtest against a null model with b = 0 (no frequency acceleration), using the sum-of-squared errors (SSE). Values in parentheses indicate bootstrap standarduncertainty in the last digit.doi:10.1371/journal.pone.0048633.t003Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 8 November 2012 | Volume 7 | Issue 11 | e48633
  9. 9. loop is a generic ‘‘developmental’’ trajectory: as an organizationages, it tends to produce violent events more and more quickly.The typical form of this relationship can be mathematicallymodeled by a power-law function, in which the delay Dt betweenconsecutive events decreases roughly like Dt!k{bwhere k countsthe cumulative number of events and b describes the strength anddirection of the feedback loop. The implication of the power-lawpattern is that large organizations are very much like ‘‘scaled up’’versions of small organizations, and in particular that size andexperience are coupled in a positive feedback loop.Across all organizations in our sample, we estimateb~1:0+0:1, indicating a linear feedback loop, which impliesthat an organization’s overall size is strongly correlated with thesize of its militant wing. This pattern is strongest for small orinexperienced organizations, e.g., those with kƒ10 events, whichcovers 87% of the 910 organizations in our sample. In contrast,highly experienced organizations seem to saturate their eventproduction rates at the daily or weekly level, which may beindicative of a tendency of large organizations to engage inmultiple types of activities, e.g., the provision of social services,criminal activities, etc., continuing to grow their militant wings.The mathematical precision of this relationship is striking, as isthe ability of our computer simulation to reproduce it. Except forRichardson’s Law for the frequency and severity of wars, fewstatistical relationships in the study of political violence exhibitsuch regularity.The power-law relation between organizational experience andproduction rate is both conceptually and mathematically similar tothe relationship between cost and cumulative production observedin manufacturing [36] or organizational learning [37,39], wheredecreases in per-item production costs or time can be described bya power law in the cumulative number of items produced. That asimilar patterns appears in the production of terrorist events issurprising, and it may not be superficial to describe terroristorganizations as a special type of manufacturing firm whoseprincipal product is political violence and whose overall produc-tion of violence is fundamentally constrained by its size.The implication is that terrorism is inherently non-amenable tomass production, i.e., it is not a scalable enterprise, perhapsbecause each event must be humanly conceived and plannedaround a particular target, tactic or environment, and there is alimit to how much this process can be automated. One implicationof this conclusion for cyber-terrorism is that even there, despite thegreat potential for automating attacks, these too will likely not bescalable without advances in general artificial intelligence.In the language of economics, we say that terrorism capital andlabor are not freely substitutable with respect to producing newevents. If the day-to-day work of event production does not requirespecialized skills, then the growth potential of an organization beextremely large because it may draw on the largest possible pool ofpotential recruits. This point suggests that conflict-level eventproduction rates should ultimately be responsive to policy andcounter-terrorism efforts that target the size and mobility of thepool of potential recruits. That is, successful ‘‘hearts and minds’’strategies [55] are likely to lead directly to lower incident rates byboth restricting the growth and reducing the size of terroristorganizations. They may not, however, eliminate the possibility ofspectacular attacks as these do not depend on organizational size.Recently, following our original work on progress curves interrorism [22], Johnson et al. [25] analyzed the timing of events inthe Iraq and Afghanistan conflicts, finding similar power-law likeacceleration curves in the delay between events. They argue thatthis pattern is caused by a kind of ‘‘red queen’’ effect–a conceptborrowed from arms races in evolutionary biology [56]–in whichtwo sides of the conflict race through some abstract space, and thetiming between events is given by how far ‘‘ahead’’ the insurgentside is in the race. In practice, however, this explanation is difficultto validate because the connection is not specified as to how real-world events and structures drive the dynamics of the abstractrace. In contrast, our explanation of the phenomena is bothtangible, general and testable: we argue that the size of theinsurgency or the terrorist group sets the tempo of the conflict.The more people there are fighting, the more frequently we willobserve events. This explanation makes direct and testablepredictions about the relationship of organizational size andfrequency of events, which we show are upheld by empirical dataon organizational sizes. (As a technical note, in the language ofphysics, the ‘‘size’’ of an organization or insurgency is an extensivevariable of the conflict system, much like area and number ofparticles are for physical systems [57]; this fact makes additionaltestable predictions of our theory.) The implication for the Iraqand Afghanistan conflicts is that the number of insurgents active inthe various provinces is the primary determinant of the frequencyof events observed there.Although the acceleration is remarkably strong, the vastmajority of organizations do not achieve high levels of experience(only 23% of groups are associated with kw10 events) or fastFigure 4. Severity of events. (A) Mean severity ,log x. of deadly attacks, with 1st and 3rd quartile, vs. group experience k. Solid line (with slopezero) shows the expected delay, from a simple regression model. (B) Conditional severity distributions Pr(x/k), showing a data collapse onto a heavy-tailed distribution, with the maximum likelihood power-law model for all severities (Richardson’s Law).doi:10.1371/journal.pone.0048633.g004Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 9 November 2012 | Volume 7 | Issue 11 | e48633
  10. 10. production rates. The progressive loss of organizations could bedue to high rates of organizational death, e.g., from counter-terrorism activities or internal conflicts [44,58], shifts away fromviolence, or a right-censoring effect on young and still activeorganizations. Significantly, the particular mode of organizationaldemise seems not to have a strong impact on the production timeof events, suggesting that the transition from development (growth)to death may happen very quickly, so that the experience curvedoes not bend upward but rather simply halts. Further explorationof the death of organizations [44,58], and how it impacts theproduction of violence, is an interesting avenue for future work.Regardless of the reason, we do not expect the feedback loop tocontinue as k??. If an organization succeeds in becoming largeenough to produce new events each day, it may function more likea stable or mature social institution, with fundamentally differentconstraints and incentives on the production of violence. Largesize and stability may also pose special risks, e.g., leading to largeror longer conflicts. On the other hand, non-violent activities, e.g.,engagement with political processes, may also become moreattractive with increased size. Exploring these possibilities is aninteresting avenue for future work.Unlike the production of events, we find no evidence of anyrelationship with the severity of attacks (H4). Rather, Richardson’sLaw–a power-law distribution in the frequency of severe events–characterizes the severity of events at all levels of organizationalsize or experience, and independent of the organization’s politicalideology.This fact clarifies ongoing efforts to identify the underlyingsocial, political or physical mechanism that generates Richardson’sLaw in terrorism. Several existing explanations assume or predicta severity-size relationship, e.g., the aggregation-disintegrationmodel of Johnson et al. [23] and [35], but these seem increasinglyunlikely given our results here, because they assume the maximumseverity of an event is proportional to the organization’s size N;thus, if N is small, the severity of events x will also be small. Thatis, in their existing form, these models predict a severity-sizerelationship that does not appear in the data. Of course, thesemodels may be adapted to produce the observed size-indepen-dence pattern, but doing so requires additional assumptions andadditional validation that may not be warranted.In contrast, two plausible explanations are not ruled out: (i) theexplanation proposed in [20], which posits a coevolutionarycompetition between states and terrorists in which event planningtime and severity are strongly related, and (ii) the explanationproposed in [24], in which population densities are broad-scaledand terrorists preferentially target high-density locations. Both ofthese explanations do not assume any relation between the severityof an attack and the size of an organization.Together, our results suggest that the total lethality of larger andmore mature groups observed by Asal and Rethemeyer [8] isprobably best explained as a natural consequence of their muchmore frequent activities, rather than as a systematic increase in thedeadliness of individual events. Policies that limit the growth of anorganization’s militant wing should lower the long-term probabil-ity of a severe event by that organization. Such growth-limitingpolicies could be described as ‘‘starving the beast’’ of the labornecessary to produce rare but highly severe events.The most productive targets of such policies will be large,established organizations with long histories of producing terroristattacks. By virtue of their size, these organizations are likely to bewell-known players in their particular conflicts and thus easytargets for specific policies. Because small organizations are equallylikely to produce severe events, policies aimed specifically at large,well-known organizations may not limit the overall risk of severeevents from all sources. For small and potentially unknownorganizations, the most effective policies may be those aimed atpreventing their formation in the first place, i.e., policies thatcurtail the acquisition of the means for and resort to violence.Lacking this, once such a terrorist cell carries out its first attack andbegins its developmental trajectory, the best action by agovernment may be an ‘‘overwhelming response’’ to encouragethrough various means the dissolution of the nascent organizationand the truncation of its growth trajectory. This policy is notwithout risk to the state, however, as certain countermeasures mayserve the terrorist’s goals [59,60].In closing, we point out that the acceleration in the frequency ofterrorist events is independent of many commonly studied factorsassociated with terrorism, including geographic location, timeperiod, international vs. domestic targets, ideological motivations(religious, national-separatist, reactionary, etc.), and politicalcontext. Our results thus demonstrate that some aspects ofterrorism are not nearly as contingent or unpredictable as is oftenassumed and the actions of terrorists may be constrained byprocesses unrelated to strategic tradeoffs among costs, benefits andpreferences. Identifying and understanding these processes offers acomplementary approach to the traditional rational-actor frame-work, and a new way to understand what regularities exist, whythey exist, what they imply for long-term social and politicalstability, e.g., large-scale violent conflicts like civil and interstatewars.Supporting InformationText S1 Supplementary Text. 1. Additional analysis of organi-zational sizes and their event frequency and severity. 2. Frequencyand severity development curves for four highly prolific organi-zations. 3. Specification and code for the simulation model. 4.Mathematical details of generic pattern in event frequencies versusexperience. 5. Robustness checks of the frequency-accelerationpattern. 6. Analysis of developmental trajectories of organizationsby political ideology.(PDF)AcknowledgmentsThe authors thank Lars-Erik Cederman, Konstantinos Drakos, BrianKarrer, James McNerney, John Miller, Mark Newman, Andrea Ruggeri,Didier Sornette, Cosma Shalizi, Brian Tivnan, Valerie Wilson andMaxwell Young for helpful conversations.Author ContributionsConceived and designed the experiments: AC KSG. Performed theexperiments: AC KSG. Analyzed the data: AC KSG. Contributedreagents/materials/analysis tools: AC KSG. Wrote the paper: AC KSG.References1. Rapoport DC (2004) Modern terror: The four waves. In: Cronin AK, Ludes JM,editors, Attacking Terrorism: Elements of a Grand Strategy, Washington D.C.:Georgetown University Press. pp. 46–73.2. Rosenfeld JE (2011) Terrorism, Identity and Legitimacy: The Four WavesTheory and Political Violence. London: Routledge.3. Enders W, Sandler T (2000) Is transnational terrorism becoming morethreatening? A time-seires investigation. Journal of Conflict Resolution 44:307–332.4. EndersW, Sandler T (2002) Patterns of transnational terrorism, 1970–1999:Alternative time-series estimates. International Studies Quarterly 46: 145–165.Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 10 November 2012 | Volume 7 | Issue 11 | e48633
  11. 11. 5. Brown D, Dalton J, Hoyle H (2004) Spatial forecast methods for terrorist eventsin urban environments. Lecture Notes in Computer Science 3073: 426–435.6. Enders WE, Sandler T (2006) The Political Economy of Terrorism. Cambridge:Cambridge University Press.7. Valenzuela ML, Feng C, Reddy P, Momen F, Rozenblit JW, et al. (2010) A non-numerical predictive model for asymmetric analysis. In: Proc. 17th IEEEInternational Conference and Workshops on the Engineering of Computer-Based Systems. pp. 311–315.8. Asal V, Rethemeyer RK (2008) The nature of the beast: Organizationalstructures and the lethality of terrorist attacks. Journal of Politics 70: 437–449.9. Enders W, Sandler T, Gaibulloev K (2011) Domestic versus transnationalterrorism: Data, decomposition, and dynamics. Journal of Peace Research 48:319–337.10. Wulf WA, Haimes YY, Longstaff TA (2003) Strategic alternative responses torisks of terrorism. Risk Analysis 23: 429–444.11. Li Q (2005) Does democracy promote or reduce transnational terroristincidents? Journal of Conflict Resolution 49: 278–297.12. Pape RA (2003) The strategic logic of suicide terrorism. American PoliticalScience Review 97: 343–361.13. Sageman M (2004) Understanding Terror Networks. Philadelpha: University ofPennsylvania Press.14. Desmarais BA, Cranmer SJ (2011) Forecasting the locational dynamics oftransnational terrorism: A network analytic approach. In: Proc. EuropeanIntelligence and Security Informatics Conference. pp. 171–177.15. Major JA (1993) Advanced techniques for modeling terrorism risk. Journal ofRisk Finance 4: 15–24.16. Kardes E, Hall R (2005) Survey of Literature on Strategic Decision Making inthe Presence of Adversaries. Los Angeles CA: Center for Risk and EconomicAnalysis of Terrorism Events.17. Richardson LF (1960) Statistics of Deadly Quarrels. Pittsburgh: The BoxwoodPress.18. Cederman LE (2003) Modeling the size of wars: From billiard balls to sandpiles.American Political Science Review 97: 135–150.19. Lacina B (2006) Explaining the severity of civil wars. Journal of ConflictResolution 50: 276–289.20. Clauset A, Young M, Gleditsch KS (2007) On the frequency of severe terroristevents. Journal of Conflict Resolution 51: 58–87.21. McMorrow D (2009) Rare Events. McLean, VA: The MITRE Corporation.22. Clauset A, Gleditsch KS (2009) Developmental dynamics of terroristorganizations. Preprint, (accessed June 17,2009).23. Bohorquez JC, Gourley S, Dixon AR, Spagat M, Johnson NF (2009) Commonecology quantifies human insurgency. Nature 462: 911–914.24. Clauset A, Young M, Gleditsch KS (2010) A novel explanation of the power-lawform of the frequency of severe terrorist events: Reply to Saperstein. PeaceEconomics, Peace Science and Public Policy 16: Article 12.25. Johnson N, Carran S, Botner J, Fontaine K, Laxague N, et al. (2011) Patterns inescalations in insurgent and terrorist activity. Science 333: 81–84.26. Holme P, Ghoshal G (2006) Dynamics of networking agents competing for highcentrality and low degree. Physical Review Letters 96: 098701.27. Gutfraind A (2010) Optimizing topological cascade resilience based on thestructure of terrorist networks. PLoS ONE 5: e13448.28. Turchin P (2012) Dynamics of political instability in the united states, 1780–2010. Journal of Peace Research 49: 577–591.29. Richardson LF (1941) Frequency of occurrence of wars and other fatal quarrels.Nature 148: 598.30. Richardson LF (1948) Variation of the frequency of fatal quarrels withmagnitude. Journal of the American Statistical Association 43: 523–546.31. Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions inempirical data. SIAM Review 51: 661–703.32. Kleiber C, Kotz S (2003) Statistical Size Distributions in Economics andActuarial Sciences. New Jersey: John Wiley & Sons, Inc.33. Mitzenmacher M (2004) Dynamic models for file sizes and double Paretodistributions. Internet Mathematics 1: 305–334.34. Newman MEJ (2005) Power laws, Pareto distributions and Zipf’s law.Contemporary Physics 46: 323–351.35. Clauset A, Wiegel FW (2010) A generalized aggregation-disintegration model forthe frequency of severe terrorist attacks. Journal of Conflict Resolution 54: 179–197.36. Dutton JM, Thomas A (1984) Treating progress functions as a managerialopportunity. Academy of Management Review 9: 235–247.37. Argote L (1993) Group and organizational learning curves: Individual, systemand environmental components. British Journal of Social Psychology 32: 31–51.38. Jackson BA, Baker JC, Cragin K, Parachini J, Trujillo HR, et al. (2005) Aptitudefor Destruction: Organizational Learning in Terrorist Groups and ItsImplications for Combating Terrorism, volume 1. Arlington: RAND Corpora-tion.39. Thompson P (2010) Learning by doing. In: Hall B, Rosenberg N, editors,Handbook of Economics of Technical Change, Elsevier/North-Holland. pp.429–476.40. Cronin AK (2009) How Terrorism Ends. Princeton NJ: Princeton UniversityPress.41. Argote L, Insko CA, Yovetich N, Romero AA (1995) Group learning curves:The effects of turnover and task complexity on group performance. Journal ofApplied Social Psychology 25: 512–529.42. Hoffman B (1998) Inside Terrorism. New York: Columbia University Press.43. Krueger AB (2007) What Makes a Terrorist: Economics and the Roots ofTerrorism. Princeton NJ: Princeton University Press.44. Jones SG, Libicki MC (2008) How Terrorist Groups End: Lessons forCountering al Qa’ida. Arlington: RAND Corporation.45. MIPT (2008) Terrorism Knowledge Base. (access dateJanuary 29, 2008).46. START (2010) Global Terrorism Database. date December 31, 2010).47. NCTC (2009) Worldwide incident tracking system. December 31, 2010).48. Mickolus E, Sandler T, Murdock J, Fleming P (2004) International terrorism:Attributes of terrorist events 1968–2003 (ITERATE). Dunn Loring, VA:Vinyard Software.49. Fishman B (2008) Using the mistakes of al Qaeda’s franchises to undermine itsstrategies. The ANNALS of the American Academy of Political and SocialScience 618: 46–54.50. Wallace MD, Wilson JM (1978) Non-linear arms race models. Journal of PeaceResearch 15: 175–192.51. Strogatz SH (2001) Nonlinear Dynamics And Chaos. Boulder, CO: Westview.52. Bhattacharjee SM, Seno F (2001) A measure of data collapse for scaling. Journalof Physics A: Mathematical and General 34: 6375–6380.53. Miller GD (2007) Confronting Terrorisms: Group motivation and successfulstate policies. Terrorism and Political Violence 19: 331–350.54. Jordan J (2009) When heads roll: Assessing the effectiveness of leadershipdecapitation. Security Studies 18: 719–755.55. Howard M (2002) What’s in a name? How to fight terrorism. Foreign Affairs 81:8–13.56. van Valen L (1973) A new evolutionary law. Evolutionary Theory 1: 1–30.57. Pathria RK (1996) Statistical Mechanics. Oxford: Elsevier Butterworth-Heinemann, 2 edition.58. Cronin AK (2006) How al-Qaeda ends. International Security 31: 7–48.59. Mueller J (2006) Overblown: How Politicians and the Terrorism Industry InflateNational Security Threats, and Why We Believe Them. New York: Free Press.60. Ganor B (2008) Terrorist organization typologies and the probability of aboomerang effect. Studies in Conflict & Terrorism 31: 269–283.Developmental Dynamics of Terrorist OrganizationsPLOS ONE | 11 November 2012 | Volume 7 | Issue 11 | e48633